Subcovers and codes on the $X_{n,r}$ curves

Abstract

In this work, subcovers ${\mathcal{X}}_{n,r}^s$ of the curve ${\mathcal{X}}_{n,r}$ are constructed, the Weierstrass semigroup $H(P_{\infty })$ at the point $P_{\infty }\in {\mathcal{X}}_{n,r}^s$ is determined and the corresponding one-point AG codes are investigated. Codes establishing new records on the parameters with respect to the previously known ones are discovered, and $108$ improvements on MinT tables are obtained.